236 ON THE REFLEXION AND REFRACTION OF SOUND. 



where we have 



, P4 



~ 'A ' 

 or by eliminating s 



Similarly, in the lower medium 



where 



PA 



The above are the known general equations of fluid mo- 

 tion, which must be satisfied for all the internal points of both 

 fluids ; but at the surface of separation, the velocities of the 

 particles perpendicular to this surface and the pressure there 

 must be the same for both fluids. Hence we have the particular 

 conditions 



d$^d$, ] . 



dx~ dx j, (where x = 0), 



As = A t s t } 



neglecting such quantities as are very small compared with 

 those retained, or by eliminating 5 and s t , we get 



dx dx 



(A). 



The general equations (1) and (2), joined to the particular 

 conditions (A) which belong to the surface of separation (yz) 9 

 only, are sufficient for completely determining the motion 6f our 

 two fluids, when the velocities and condensations are independent 

 of the co-ordinate z, whatever the initial disturbance may be. 

 We shall not here attempt to give their complete solution, which 

 would be complicated, but merely consider the propagation of a 

 plane wave of indefinite extent, which Js accompanied by its 

 reflected and refracted wave. 



